In this work, we employ an iterative version of QPE algorithm (IQPE) [1]}, [2]}, and opt for an alternative way for preparing its input reference state by using the VQE algorithm with the UCC ansätz. We refer to this approach hereafter as IQPE over VQE. A schematic of the approach is given in Fig. REF . We pick IQPE over traditional QPE, in view of many ancilla qubits that are required for the latter, which in turn makes computations very expensive. To the best of our knowledge, there is one other work in literature, where the authors independently suggest QPE over VQE, but they do not study the effect of various VQE parameters in the initial state preparation [3]}. In this work, we systematically tune the number of VQE iterations, and the choice of the initial guess parameters, and its connections to the probability of successfully landing on the right state when fed as an input to the IQPE algorithm. We will demonstrate that a multi-determinantal reference state meticulously prepared using the VQE algorithm is likely to have a superposition of all the dominant determinants of the FCI wavefunction, and thus we anticipate that one can systematically tune it to have considerable overlap with the exact eigenstate of the Hamiltonian, even in strong correlation regimes. We then demonstrate the strength and applicability of this method by carefully selecting a physical system that displays varied electronic complexity across its PES. After generating the PES and studying the precision of our final results with the number of IQPE iterations, we show that our approach provides a good and systematically improvable probability of success to land on the correct state. We also extend our analyses by studying the scenario with Qiskit's QASM backend, where sampling comes into play.
